Firstly, note you have similar triangles ABC and ABD and BCD. This is because they have a common angle and a right angle in each. So that ABC and BCD are similar because C is common. ABD and ABC are similar because angle A is common.
Secondly, because they are similar, their sides are in proportion. Eg x/12 in ABD = 12/2x in BDC (look at the angles in each which are equal, to see the sides that correspond).
This means 2x squared = 144. So x^2 = 72 so x= 6 root 2 which is 'c'
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